I was lucky enough to get an assisted place just before they were abolished. My mum was a single mum and there was no way she could've paid the full amount for me to go to a private school.
You also have to remember that, although your child may be top of the class at her current school, there is a high chance of her not being so at a private school. I was the same as her in my state primary, used to ask for homework, was in top sets, etc and when I joined the private school I was just an average student, no longer "1 of the best", had to work a hell of a lot harder just to maintain average marks. It was a lot of hard work and pressure for me to go to that from being "a top student"
Secondly, You still end up having an awful lot to pay out. Uniform (including things like tennis racquets, hockey sticks, etc) extra music lessons or possibly tuition to help your daughter maintain her grades if necessary. School trips (our school had an annual ski trip available, as well as other trips to theatres, Barcelona, London, Kenya, Ecuador, etc) As you do get to the point where you don't want her missing out on things like that but they can be difficult to afford.
You also have to take into account how you will feel if after a year or 2 at a private school she decides she can't cope with the pressure or is not at all happy. I do know of some parents who have guilted their children into staying because of "how good the school is" and "the opportunity they have been given." I was lucky as my mum never put any pressure on me. It was up to me to sit the entrance exam and when offerred a place it was up to me whether I accepted or went to the local comp with all of my friends. And throughout my school career, I always knew it was down to me. If I wanted to leave and go join my mates, she would've let me, as long as I was happy.